Error estimates for a mixed finite element discretization of some degenerate parabolic equations

Radu AF, Pop IS, Knabner P (2008)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2008

Journal

Publisher: Springer Verlag (Germany)

Book Volume: 109

Pages Range: 285-311

Journal Issue: 2

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2008/2008_RaduPopKn_ErrorEstimatesForAMixedFiniteElementParabEqua

DOI: 10.1007/s00211-008-0139-9

Abstract

We consider a numerical scheme for a class of degenerate parabolic equations, including both slow and fast diffusion cases. A particular example in this sense is the Richards equation modeling the flow in porous media. The numerical scheme is based on the mixed finite element method (MFEM) in space, and is of one step implicit in time. The lowest order Raviart-Thomas elements are used. Here we extend the results in Radu et al. (SIAM J Numer Anal 42:1452-1478, 2004), Schneid et al. (Numer Math 98:353-370, 2004) to a more general framework, by allowing for both types of degeneracies. We derive error estimates in terms of the discretization parameters and show the convergence of the scheme. The features of the MFEM, especially of the lowest order Raviart-Thomas elements, are now fully exploited in the proof of the convergence. The paper is concluded by numerical examples. © 2008 Springer-Verlag.

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APA:

Radu, A.F., Pop, I.S., & Knabner, P. (2008). Error estimates for a mixed finite element discretization of some degenerate parabolic equations. Numerische Mathematik, 109(2), 285-311. https://dx.doi.org/10.1007/s00211-008-0139-9

MLA:

Radu, Adrian Florin, Iuliu Sorin Pop, and Peter Knabner. "Error estimates for a mixed finite element discretization of some degenerate parabolic equations." Numerische Mathematik 109.2 (2008): 285-311.

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